Journal of Research of the National Bureau of Standards
AbstractThis paper presents a method of solving for Fourier coefficients where the dependent variable can be expressed as a piecewise continuous function, when various conditions of continuity and smoothing are assumed. An example is included to show the effect of smoothing in the region of a discontinuity for a system composed of two materials that exhibit a discontinuity at their interface and surrounded by a third material which does not have a discontinuity. An advantage to be gained from smoothing is an increase in the convergence of a finite Fourier series representation of a piecewise continuous function in the region of the discontinuities.
CiteJ. Res. Nat. Bur. Stand. Sec. C: Eng. Inst., Vol. 71C, No. 2, p. 93
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